x_{0}x*x-x*x+x=1 eching

$$x _ { 0 } x \cdot x - x \cdot x + x = 1$$

x_0 uchun yechish

$$x_{0}=1-\frac{1}{x}+\frac{1}{x^{2}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x_{0}x^{2}-xx+x=1$$

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$x_{0}x^{2}-x^{2}+x=1$$

x^{2} ni ikki tarafga qo’shing.

$$x_{0}x^{2}+x=1+x^{2}$$

Ikkala tarafdan x ni ayirish.

$$x_{0}x^{2}=1+x^{2}-x$$

Tenglama standart shaklda.

$$x^{2}x_{0}=x^{2}-x+1$$

Ikki tarafini x^{2} ga bo‘ling.

$$\frac{x^{2}x_{0}}{x^{2}}=\frac{x^{2}-x+1}{x^{2}}$$

x^{2} ga bo'lish x^{2} ga ko'paytirishni bekor qiladi.

$$x_{0}=\frac{x^{2}-x+1}{x^{2}}$$

1+x^{2}-x ni x^{2} ga bo'lish.

$$x_{0}=1-\frac{1}{x}+\frac{1}{x^{2}}$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4x_{0}-3}-1}{2\left(x_{0}-1\right)}\text{; }x=-\frac{\sqrt{4x_{0}-3}+1}{2\left(x_{0}-1\right)}\text{, }&x_{0}\neq 1\\x=1\text{, }&x_{0}=1\end{matrix}\right,$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{4x_{0}-3}-1}{2\left(x_{0}-1\right)}\text{; }x=-\frac{\sqrt{4x_{0}-3}+1}{2\left(x_{0}-1\right)}\text{, }&x_{0}\neq 1\text{ and }x_{0}\geq \frac{3}{4}\\x=1\text{, }&x_{0}=1\end{matrix}\right,$$